C₈×C₄₃ #66807

order	344
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₃×C₇ (order 168) · Inn(G) = C₁ · Out(G) = C₂³×C₃×C₇
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₄₄
abelian	C₈×C₄₃

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 344

A minimal faithful permutation representation — 1 generator on 51 points:

(1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51)

344 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(344, 2);